Reference

Extra principal: where the leverage actually is.

A small recurring overpayment compounds in a way that surprises most borrowers. The leverage is real and asymmetric — the same dollar saves more interest in year 1 than in year 20.

Why an extra dollar today is worth more than an extra dollar later

Every dollar of extra principal paid in period k reduces the outstanding balance from period k+1 onward. The interest charge in each subsequent period is the balance times the rate, so eliminating a dollar from the balance eliminates the interest that dollar would have generated for the remaining life of the loan.

For a 25-year monthly loan at 6%, an extra dollar paid in month 1 saves (1.005)²⁹⁹ − 1 ≈ $3.46 in interest. The same dollar paid in month 250 saves (1.005)⁵⁰ − 1 ≈ $0.28. The leverage decays exponentially.

The closed-form approximation

For a small extra payment E made every period for the life of the loan, the interest savings approximate to:

interest_saved ≈ E · n · (1 − (PMT / (PMT + E)))

where n is the original number of periods. The simulation in the calculator is exact and avoids approximation error; the formula above is useful only as a back-of-envelope check.

Reference: extra payment effect by horizon

$200,000 loan at 6%, monthly schedule, $100/month extra payment, by original term:

Original term	Original interest	Interest with $100 extra	Savings	Time saved
15 yrs	$103,800	$96,200	$7,600	1.0 yr
20 yrs	$143,800	$128,300	$15,500	1.9 yr
25 yrs	$186,400	$159,500	$26,900	3.1 yr
30 yrs	$231,700	$192,000	$39,700	4.7 yr

The same $100/month extra saves $40,000 over 30 years and only $7,600 over 15 years. Longer original terms have more interest to compound away, so extra payments produce larger absolute savings.

The prepayment-privilege trap

Most fixed-rate Canadian mortgages cap annual prepayment at 10–20% of original principal. Exceed the cap and the lender charges an Interest Rate Differential (IRD) penalty — on a $300,000 loan with a 4.5% rate and 3 years remaining at the time of overpayment, the IRD penalty is typically $4,000–$8,000. The arithmetic of overpaying is great within the privilege limit and frequently negative outside it. Read your contract.

Lump sum vs. recurring

A one-time lump-sum payment of $12,000 in year 1 saves more interest than $1,000/month for 12 months in year 1 — but only marginally (the difference is roughly the interest accrued on the remaining $11,000 over the year). For most borrowers the choice is determined by cash-flow availability, not optimisation.

A lump-sum bonus deployed against the mortgage in year 1 of a 25-year loan at 6% saves roughly $2.46 per dollar paid. The same lump sum invested at a 7% real return for 25 years grows to $5.43 per dollar — a higher gross return, but exposed to market risk and liquidity loss. The trade-off is real; we don't pretend either side dominates universally.

How to use the calculator for this

Enter the loan in the main calculator. Note the baseline interest. Re-enter with your planned extra payment. The savings figure that appears is the interest avoided. Repeat with different extra-payment amounts to find the sweet spot for your cash flow.